How can I add an image to a texture in Cycles?
Idle Chit-chat

I don't see any reason why you should not be able to simply unwrap the eyes and add in your texture, as I said in my comment. I will, however, elaborate here.

Materials

I will use a sphere to represent the eye (smooth shading), and the following eye texture from Google (full size linked).



With the sphere selected, go to the Materials tab in the Properties panel. + New a material to the sphere. Go into the Node editor, and use the setup shown.



Now, go to the sphere in the 3D Viewport. Tab into edit mode, Numpad 1 to front view, and Numpad 5 to orthographic view. Press U and select Project from View (Bounds). Split the screen into a 3D Viewport and a UV Image Editor by dragging the marks in the top-right corner to the left. Make sure you are still in edit mode. Open the image of the eye through the toolbar at the bottom of the UV Image Editor. The orange should already be aligned over the eye.

Final Notes

For whatever reason, the eye did not show up right from the pure UV editing, so I had to add the Mapping node to the node setup.

Here is the .blend file: